Accurate estimation of rare precipitation events requires methods that capture complex spatial and temporal extremal dependence, especially when extrapolation is needed. This paper presents our team’s contribution to the EVA (2025) Conference Data Challenge, which involves predicting the expected number of high-threshold excesses on a 5 × 5 spatial grid over 165 years (1850-2014). The targets consider several types of extreme events, including simultaneous extremes at all locations, excesses at multiple sites on the same date, and consecutive-day excesses across subsets of locations. We approach all three targets using a single model, in which temporal dependence is captured through location-specific marginal models, and spatial dependence is implicitly accounted for via a conditional multivariate extreme value model. This modelling strategy, which earned joint second place overall, is broadly applicable to other problems involving rare events with complex spatio-temporal dependence structures.
This paper presents the approach of Team Moscow State to solving the tasks of the EVA (2025) Conference Data Challenge. Although the challenge tasks were originally formulated in a multivariate setting, they can be reformulated as problems of univariate statistics of extremes, which largely determined our approach to their solution. It relies on a unified framework that combines classical techniques of statistics of extremes with the recently proposed block quantiles method.
The problem of detecting the existence of a changepoint in a data sequence and of identifying its position is challenging when the focus is on extreme events and the distribution of data is heavy-tailed. In this setting, we recall several existing techniques, and then we propose a novel robust semi-parametric approach to changepoint identification that does not require the likelihood function. The changepoint is estimated as the position of the maximum of a statistic inspired by classical ANOVA to contrast the tail behavior of data to the left and right of all changepoint candidates. It is shown that the estimator consistently identifies the true changepoint under mild assumptions when the sample size increases. In numerical experiments, the novel method shows reliable finite-sample behavior for various simulation settings and is very competitive in comparison to the alternative changepoint identification approaches from the literature, especially for small sample sizes. Finally, the utility of the method is highlighted by identifying interpretable changepoints in three real-data applications: very large motor insurance claim amounts for a French administrative region with age as covariate; daily Bitcoin cryptocurrency price data and daily returns of stocks of the Boeing company both with time as covariate.
While random probability measures have a long tradition in probability and statistics, little is known about their tails. The few available results are derived using subordinators, and therefore only apply to measures that can be represented as normalized subordinators, such as the Dirichlet process. Our work breaks this barrier, by exploiting the stick-breaking representation to construct a new family of transport maps that preserve the decay of tails. Drawing on recent developments on regular variation and on subordinator theory, the new family of maps allows us to establish that the right tail of a Pitman–Yor process is heavy-tailed if the centering distribution is itself heavy-tailed; the Dirichlet process is the only member of this class that fails to obey this convenient property. Asymptotic envelopes for the tails of the Pitman–Yor processes are also derived. Finally, we discuss some consequences of the main results, including aspects related to the posterior distribution.
We correct and generalise Theorem 3 in Novak (2019), and formulate an open question.
